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~home||
Overview
ELECTRONICS WORKBENCH
(C) 1988, 1991 Interactive Image Technologies Ltd.
All rights reserved.
An Electronic Analog Circuit
Design and Simulation Program
────────────────────────────────────────
{■ What you can do with EWB:purp}
{■ Parts of the screen:scrn}
{■ Building a circuit:wksp}
{■ Simulating a circuit:go}
{■ File operations:F9}
{■ Program controls:ctrl}
{■ List of topics:tpx}
Point and click to get more.
~purp||
Purpose
Electronics Workbench can be used to
■ {construct:wksp} a schematic for an electronic
circuit
■ {simulate:go} the activity of that circuit
■ display the circuit activity on simulated
test instruments:inst}
■ and {print:prt} a copy of the schematic, the
instrument readings and parts list
~scrn||
Appearance
The program models a workbench for electronics.
The large central area on the screen acts as a
{breadboard:wksp} for circuit assembly.
On the right side of this {workspace:wksp} is a
{bin of parts:bin}.
Above the workspace is a shelf of
{test instruments:inst} and {program controls:ctrl}.
You may wish to read about {common operations:ops}
for the {workspace:wksp}.
{List of topics:tpx}
~inst||
Instruments
To use the {test instruments:ti1}
{■ put them on the workspace:wksp}
{■ attach wires to test points:ti2}
{■ zoom them open:ti3}
to adjust the controls
to see the display
{instruments:ilst}
~ti1||
Test instruments
The left end of the shelf at the top of the screen
holds test instruments.
Handle the icons for the instruments just as you
do parts, except that there is only one copy of
each instrument.
To use the test instruments, you must put them on
the {workspace:wksp} and {run wires:ti2} from them to the
points in the circuit you wish to measure.
~ti2||
Attach instruments
Attach {wires:wir} from the terminals of the instrument
icon to points where you want to measure values in
the circuit. Use the {connector} to put test points
in the circuit.
~ti3||
Adjust and read
{Zoom:f7} instruments on the {workspace:wksp} open
by highlighting them and pressing F7 or double
clicking. Now you can read their displays,
{adjust:sps} their controls, or {drag:drg} their faces
around.
{See each instrument for details.:ilst}
~wksp||
Workspace
To build a circuit
{■ pick components from the parts bin:pnt}
{■ place them on the workspace:wksp}
{■ wire the components together:wir}
{■ attach test instruments:inst}
{■ click GO to activate the circuit:go}
When an object is {selected:sel} you can {drag:drg} it,
connect {wires:wir} to other objects, or perform
various {menu} operations on it.
You can {scroll the workspace:scrl} to build a
large circuit.
{common operations:ops} {mouse} {tips}
~tips||
Tips
When you lay out a circuit, leave room between
parts to insert connectors or other parts easily.
{Rotate:f8} parts to get the layout you want.
You can turn on a {grid} that objects will line up
with. All terminals of all parts will be on grid
lines if you choose grid size 1 -- this eliminates
small kinks in the wires.
{Wires:wir} may find different routes if they start
from the other end. This can help make a nice
appearance for {printing out:prt}.
Use {macros:f5} to make parts you don't have, such
as gates with three or more inputs, or to build a
complex circuit out of smaller modules. You must
{save:lsp} the parts bin with the macro and use
the same bin when you reload circuits containing
the macro in the future.
~scrl||
Scrolling the workspace
The circuit may be considerably larger than the
area of the screen. The workspace has an area of
approximately three by three screens.
{Point:pnt} to the {scroll:scri} icon in the upper
right and hold the {first mouse button:m} to move the
circuit around. The scroll icon also indicates the
relative position of the visible portion in the
workspace. When you move a wire on the workspace
beyond the edge of the screen, the workspace
scrolls to keep up with it.
The workspace will not scroll when an
instrument face is {zoomed:f7} open.
~ops||
Common operations
Electronics Workbench operates by direct
manipulation of objects on the screen. You can do
all operations in the program without typing
commands. Function keys provide shortcuts to most
operations.
To do anything with an object in Electronics
Workbench, {point:pnt} to it with the tracker to
highlight it.
Now press the {first mouse button:m} and the
simplest thing you can do with the lighted object
happens. For most objects, this means you can
{drag:drg} it with the tracker.
Click the {last mouse button:m} to {select an:ps}
{object permanently:ps} and then pull down the
{menu}. This lets you do things such as {label:f6},
{rotate:f8}, {move:f4}, {copy:f3} or make a
{macro:f5} of one or many parts.
Shortcut: Point to an object and press the
function key listed in the {menu} to do most
operations.
~mouse|m||
About the mouse
In the descriptions here, the left mouse button
will be referred to as the "first mouse button"
and the right will be called the "last button."
For right-handed users, this means the first
button is controlled with the index finger and the
last is controlled with the ring or middle finger.
This should be less confusing to most readers,
since the mouse is used with one hand.
It also allows left-handed persons to use a
utility (if available, such as Logitech's CLICK
program) to reverse the buttons and still follow
the instructions.
~pnt||
Pointing with the tracker
The mouse controls an arrow on the screen,
called the "tracker" or the "cursor."
Move the tracker onto a component to make it
highlight. Press and hold the {first mouse:m}
{button:m} to make the component move with the
tracker. Release the button to leave the component
in place on the {workspace:wksp}.
Connect parts with wires by pointing to a terminal,
pressing the first mouse button and stretching the
wire to another terminal to highlight it, and then
releasing the button.
~sel||
Selecting objects
Throughout these instructions, we refer to actions
on selected objects. To keep the explanations
simple, "select" may refer to any of the
following actions:
selecting things {one at a time:ot}
{permanently:ps}
or {in a block:bs}.
Double clicking --
Clicking the mouse button twice quickly is a
shortcut for {zooming:f7} and loading files.
~ot||
Selecting one at a time
When you move the cursor into an active area or
near an active object, the area or object
{highlights:pnt} to indicate that it is selected
and ready for action.
The {first mouse button:m} causes an appropriate
action to happen, such as picking up a component,
stretching a wire, or moving a {spin selector:sps}.
Function keys act on an object that is selected
by {pointing:pnt}. These other keys perform the
same functions as {menu} items.
~ps||
Selecting permanently
Point to an object and click the {last mouse:m}
{button:m} to select an object "permanently," i.e.
until it is deselected by clicking the button
while not touching any component.
Select an object permanently to use the {menu}
operations.
You can select several parts this way for mass
{cutting:f2}, {moving:f4}, {copying:f3},
{rotating:f8} or {labelling:f6}.
~bs||
Selecting in a block
You can select a group of parts for many
operations -- hold the {last mouse button:m} and
move the tracker to stretch a rectangle that
selects components in its range. Release the
button and the parts within the rectangle will
be selected.
This is useful for {cutting:f2}, {copying:f3},
{moving:f4} and making {macros:f5}. It works for
{rotating:f8} and {labelling:f6}.
~drg||
Dragging objects around
To move a single object, you can {point:pnt} to
it with the tracker and press and hold the
{first mouse button:m}. Now you can drag the part,
instrument icon, instrument face, or dialog box
around on the {workspace:wksp}.
Release the button to leave the object in its new
place. Objects may be freely dragged about on the
screen this way. Objects may overlap, but you may
lose track of wires this way.
~wir||
Wires
■ {Connect:cct} components by selecting a terminal
and stretching a wire to its destination.
■ To {disconnect:dct} parts, simply select a
terminal and move the tracker before
releasing.
■ {To connect wires to each other:wct}, use a
{connector} from the parts bin.
~cct||
Connecting parts
To connect components or instruments with wires,
{point:pnt} to a terminal on the object. When the
terminal is highlighted, press and hold the {first:m}
{mouse button:m} while moving the tracker. A "rubber
band" line appears, with one endpoint attached to
the terminal and the other attached to the tracker.
Move the tracker to highlight the destination
terminal and release the button.
The wire finds a route between the terminals
automatically, making sure it does not go on top of
other components and does not overlap other wires.
Wires cross at right angles without connecting.
You can insert components into wires by
aligning their terminals with the wire and
releasing.
~wct||
Joining wires
A {simple junction:connector} is included in the
parts bin. Use it to:
■ make direct connection between wires
■ attach test {instruments:inst}
Like all other circuit elements, these connectors
must be in a circuit before it is simulated with
{GO} in order to have values. Put connections
along the wires in your circuit for test points
while you build it.
If you {rotate:f8} or {move:f3} a component that
is already wired in place in the circuit, the
wires automatically connect to the new position.
Moving a component, even accidentally, does not
undo prior work.
~dct||
Cutting wires
Remove components or instruments from the
{workspace:wksp} by {dragging:drg} them to the parts
bin or top shelf areas. Disconnect wires by
selecting a terminal, holding the first mouse
button, and releasing away from any terminal.
~bin||
Parts bin
The parts bin contains the {supply of parts:com}.
You can {label:f6} components in the parts bin, so
you can put many components of the same value into
the circuit easily. You can change the value in
the parts bin without affecting parts already on
the {workspace:wksp}. {Cut:f2} parts from the bin
by {pointing:pnt} to them with the tracker and
pressing F2.
If you {cut:f2} parts from the bin or add
{macros:f5} to it, be sure to save the new parts
bin under a new name. When you have a special
parts bin loaded (or have changed the bin),
you will be prompted to save it when you save
the circuit.
~go||
Activating the circuit
The GO icon on the command bar is used to simulate
the activity of the circuit.
{■ simulation:sim} {■ errors:err}
~sps||
Spin selector
Many of the controls on the instruments are spin
selectors. A box containing a number highlights
when you point to it. Press and hold the
{first mouse button:m} to change the number
through a range of values by moving the mouse.
Release the button on the desired number to set
the value.
~keys||
Special keys and editing
{File:f9} boxes, {label:f6} boxes,
the {word generator} and the {truth table}
have text fields you can type into.
On the boxes, a text cursor appears at the
beginning of the first line.
On the instruments, you must activate the text
cursor by {pointing:pnt} to the text field and
clicking. Click outside a text field to remove
the cursor and make the field inactive.
{The editing keys:ky1} that move the cursor and
edit the text work as expected in a text field.
~ky1||
Editing keys
The cursor control keys move right and left, and
up and down if appropriate. HOME and END move the
cursor to the beginning and end of the line.
CTRL-END deletes text from the cursor position to
the end of the line. ENTER acts as clicking ACCEPT
would. TAB and SHIFT-TAB move forward and back
through the fields if there are more than one.
~ctrl||
Program controls
Icons on the upper right of the screen control
fundamental operations in the program:
■ The {Menu} contains the program commands.
■ The two {scroll boxes:scri} control the {parts bin:bin}
and {workspace:wksp}.
■ The {GO} icon starts simulating the circuit.
The rectangle towards the middle of the shelf
displays the filename for the circuit. When you
load a circuit the filename appears here. You may
optionally type into this {text field:keys} after
{selecting:sel} it. You will be prompted for a
filename to save to when you use Files (F9) from
the {menu}.
~scri||
Scroll boxes
The scroll boxes allow you to move the
{parts bin:bin} (box on the far right)
or the {workspace:wksp}.
Point to the scroll box, press and hold the {first:m}
{mouse button:m} and move the tracker to scroll the
area.
~menu||
Menu operations
{help -- f1:f1}
{cut -- f2:f2}
{copy -- f3:f3}
{move -- f4:f4}
{macro -- f5:f5}
{label -- f6:f6}
{zoom -- f7:f7}
{rotate -- f8:f8}
{file -- f9:f9}
{preferences -- f10:f10}
{clear:clr}
{print:prt}
{quit}
~f1||
Help -- F1
Press F1 or choose Help from the {menu}
to get help with Electronics Workbench.
If an object is selected when help is
called, it will refer to the selected object. If
help is called with no object selected, a list of
topics is presented. Click on an entry and a window
containing information will open.
Within the help system, {boldface:f1} marks
cross-references to other topics. You can select
these words to open another window on the new
topic. More than one help window may be open at
once. You can move the windows around on the
{workspace:wksp} and the workspace is usable while
the windows are open.
~f2||
Cut -- F2
Cut parts that are {permanently selected:ps}
from the {workspace:wksp} with the {menu}
selection or F2. This is useful for removing
several parts at once from the circuit.
You can {drag:drg} individual parts back to the
{parts bin:bin} and release them; they need not be
disconnected beforehand.
~f3||
Copy -- F3
To copy a part on the {workspace:wksp} to another
place, {select it permanently:ps} and choose Copy
from the {menu} or {point:pnt} to it and press F3.
To put lots of the same part on the workspace,
point and copy it with F3.
Copies of parts have the same {labels and:f6}
{values:f6} as the original, so you can make many
copies with the same value easily by assigning a
value before copying. Groups of parts may be
selected and copied to other places in the
circuit.
~f4||
Move -- F4
You can move a group of {selected:sel} parts with
the {menu} selection or F4. If there is no room
for them on the {workspace:wksp} when released,
they will bounce back to their source.
~f5||
Macro -- F5
You can combine circuits or sub-circuits
into a macro block.
You can make new parts, such as logic gates with
more inputs, or develop large circuits with
smaller modules.
{select parts:mc1} {edit macros:mc2} {save parts:mc3}
~mc1||
Making a macro
Select the components you want on the
{workspace:wksp} and choose Macro from the {menu}.
You should give it a name and you must decide
whether to copy the parts or move them from the
workspace into the macro. The macro is then
automatically placed into the {parts bin:bin} in a
standard package.
~mc2||
Editing a macro
You can edit the contents of the macro by
{zooming:f7} it open on the workspace. Stretch
wires to the sides of the box to make terminals.
Macros can have labels, which are displayed on the
icon.
~mc3||
Save macros
To use macros in a future session, you must save
the parts bin containing them and reload it when
the circuit is used again. Macros that are not in
the current parts bin will be empty and not run.
~f6||
Label -- F6
Use this
■ to {give values:gvl} to analog parts
■ to {label parts:lbp}
■ to {label the circuit:lbp}
■ to {define models:dfm} of analog parts
Type values into the "Value" text field.
Not all components will have value text fields.
Type labels into the "Label" text field.
Choose models with the "Model" {spin selector:sps}.
Click on the "Model" button to {alter analog models:dfm}.
Analog parts must have values for the circuit
simulation to work. Most parts do not have
default values, though the transistors and
diodes have typical useful values.
To {show:slb} labels, values and models on
the workspace, use the {Preferences:f10} menu.
You can {select a block:bs} of components and then
label them sequentially by choosing Label,
assigning values or labels in turn, and cancelling
the operation when desired or finished.
~gvl||
Analog values
Give values to components by {selecting:sel} them
and choosing Label from the {menu} or pressing F6
when the part is highlighted. Enter the desired input
into the appropriate boxes from the keyboard. If
you click ACCEPT without entering values, the
minimum acceptable value will be given to the part.
Labels and values can be given to parts in the
circuit or in the {parts bin:bin}.
To change the values of some parts such as the
transistor, you must click on the {"Model" box:dfm}
and adjust parameters appropriately.
You can give values to the components in the parts
bin, so that many parts with the same value can be
used. Changing the value of the part in the bin
does not change values already in the circuit.
~lbp||
Text labels
You can put labels up to six characters long on
components, including connectors.
You can give a label to the entire circuit by
selecting Label or F6 with no parts selected.
The circuit label can be {printed:prt} out with
the circuit. It is placed beside the schematic on
the printed output.
~dfm||
Analog models
Clicking on the "Model" button opens a box
containing the component parameters. Type the
desired value in the text field beside the
standard abbreviation. The parameters for each
part are explained in the User Manual.
Models are global, so you can change values for
a model and the changes affect every copy of that
model in the circuit. Models are saved with the
parts bin.
The "Model" {spin selector:sps} displays the list
of available models.
Next to "New name" is a text field in which
either a new name for the existing model, or the
name of a new model can be entered.
In order to change the name of the displayed
model, without generating a new model, specify
the desired name in the "New name" text field
and click on "Change name".
If a new name is specified, "Save changes" will
generate a model with this new name, having the
specified parameters.
If no new name is specified, "Save changes" will
save the new model parameters for the existing
model.
If a model is no longer useful and you wish
to remove it from the list of available models,
click on "Delete".
While the model box remains active, you can
edit, add or delete as many models from the
model list as you wish.
When you have completed your edits, and you
have located the model which you wish to assign
to the part being labeled, click on "Accept".
It is not necessary to click on "Save changes"
first, as this is automatically done.
If you have performed edits, but do not wish
to change the model of the part being labeled,
click on "Cancel".
~f7||
Zoom -- F7
Zoom works on {instruments:inst} or {macros:f5}.
{Permanently select:ps} the instrument or macro
and choose Zoom from the {menu} to show an
enlarged view. To close the instrument or macro,
do the same thing.
Shortcut: {Point:pnt} and press F7
or {double click:sel} the mouse button
~f8||
Rotate -- F8
You can rotate most of the components to achieve
nearly any desired layout on the {workspace:wksp}.
Each time you select a part and rotate it, it
turns 90 degrees clockwise. {Select:sel} a part or
parts and choose Rotate from the {menu} or press F8.
The {ground} symbol does not rotate.
Transistors rotate 90 degrees the first time
you select Rotate, then reverse their symmetry for
the remaining two positions. This enables you to
follow standard drafting conventions when laying
out a circuit.
~f9||
File -- F9
To save or load a circuit or a set of parts,
select File from the {menu} or press F9.
Now you get a file selector box where you can
{load parts:lsp} or {circuits:lsc}, or {save:lsp}
{parts:lsp} or {circuits:lsc}.
The full path to the current directory is
displayed across the top of the file list. Each
name in the path will act as a pull-down menu
showing the other directories at that level when
you point and press the {first mouse button:m}.
This lets you change directories to load and save
files easily.
You can save patterns for the {word generator}
from the instrument face.
~lsc||
Loading and saving circuits
When you choose to load or save a circuit from
the file selector box, you get a list of existing
circuits.
■ To save a new circuit, type a name (up to
eight characters) into the lower empty box
and click on SAVE.
■ To load a circuit file, select a name from
the scrolling list or type the name in the
lower box and click on LOAD.
ENTER after typing is a shortcut to SAVE.
Double click on the file in the list to LOAD.
Tip: Save the circuit with the test instruments
wired in place and the settings of the instruments
will be saved too.
~lsp||
Loading and saving parts
Special parts files are useful to collect special
{macro:f5} circuit components or to control
{values:f6} of parts for teaching assignments.
When you save a circuit, you will be prompted to
save the parts bin. If you save the bin, it will
automatically load with the circuit.
BE CAREFUL NOT TO SAVE A PARTS BIN OVER A DIFFERENT
ONE WITH THE SAME NAME. THE NAME OF THE BIN IS
DISPLAYED ON THE DIALOG BOX. YOU WILL BE WARNED IF
THE FILE EXISTS. IF YOU DO NOT SAVE THE PARTS BIN,
THE CIRCUIT WILL STILL LOAD, BUT SOME PARTS MAY NOT
WORK.
When you choose to load or save a parts bin
from the file selector box, a list of existing
bins in the current directory appears.
■ To save a new parts bin, type a
name (up to eight characters) into the
lower empty box and click on SAVE.
■ To load a parts bin, select a name
from the scrolling list or type the name
in the lower box and click on Load.
ENTER after typing is a shortcut to SAVE.
Double click on the file in the list to LOAD.
~grid||
Grid
Using the {Preferences:f10} menu, you
can control a gridsnap feature that causes
components to align themselves automatically.
The grid is active by default.
You can turn the display of the grid on
or off when it is active.
Only at the smallest grid size will all
terminals on all objects align to grid points.
~sgr||
Show grid
When the {grid} is turned on, you can display it
if you want by clicking on the button on the
{Preferences:f10} menu.
~slb||
Show labels
From the {Preferences:f10} menu,
set this on to display {labels:f6}
assigned to parts.
~svl||
Show values
From the {Preferences:f10} menu
set this on to display {values:f6}
assigned to parts.
~clr||
Clear
From the {menu}, select this to clear the
{workspace:wksp}, the circuit name, and the
readings on instruments. A dialog box asking
confirmation of the action will appear.
~prt||
Print
Select Print from the {menu} to get the circuit
printed on a dot-matrix printer. A menu of options
will appear to
■ print the circuit
■ the faces of the {test instruments:inst},
■ and a parts list.
You can {make a label:f6} for the circuit using
Label from the menu or pressing F6 when nothing
else is selected. It is a free-form {text:keys}
{field:keys} of six lines by twenty-five
characters.
Click on "Change Printer Configuration" to
open the "Printer Configuration" box.
Use the "Printer" {spin selector:sps} to choose
your printer from a list. If your printer does
not appear, consult the User Manual.
The "Printer Port" spin selector allows you to
choose the destination of the output, including
a disk file.
You can spin select the "Paper Length."
The displayed pathname is a selector that
controls the location of the output file. Point to
a part of the pathname and press and hold the first
mouse button to pull down a menu of directories.
Type a filename into the "Output file name"
text field.
~quit||
Quit
Selecting Quit from the {menu} exits
the program and returns to the
operating system. A confirmation box
appears.
~connector||
Connector
Use a connector to {join two wires:wct}. Otherwise,
wires cross without electrical connection.
It is good practice to place connectors into a
circuit at various test points before
{simulation:sim} so you can make readings at
various places in the circuit.
~ground||
Ground
Ground is the reference point for relating
electric {voltage:v} levels wherever electricity is
used. The ground symbol from the {parts bin:bin}
provides this reference.
In digital {simulation:sim}, ground is used for a 0
level.
Analog circuits require a common ground to work
properly and give consistent results. Be especially
careful to have both sides of a transformer grounded.
It is important to ground analog instruments to
obtain accurate results.
The analog simulation will give an error message
if the circuit and instruments are not properly
grounded.
{More information about ground:mrgn} is available.
~mrgn||
Ground -- general information
A voltage measurement is always referenced to some
point, since a voltage is actually a "potential
difference" between two points in a circuit.
The concept of "ground" is a way of defining a
point common to all voltages, one which we agree
represents the common reference for all the
circuits. It represents "0 Volts"; all voltage
levels around the circuit are positive or negative
when compared to that reference point. In power
systems, the planet Earth itself is used for this
reference point (most home power circuits are
ultimately "grounded" to the Earth's surface for
lightning protection). This is how the expression
"earthing" or "grounding" a circuit originated.
Most modern power supplies have "floating" +/-
outputs, and either output point can be defined as
ground. These types of supplies can be used as
positive (with respect to ground) or negative
power supplies. In floating power supply circuits,
the positive output is often used as the voltage
reference for all parts of the circuit.
~tpx||
Topics available
{ac voltage}
{ammeter}
{analog circuit simulation:sim}
{analog components:com}
{analog error conditions:err}
{analog instruments:ilst}
{analog precision:apre}
{battery}
{Bode plotter}
{bulb}
{capacitor}
{clear:clr}
{common operations:ops}
{components:com}
{connector}
{copy -- f3:f3}
{current source:ctsc}
{cut -- f2:f2}
{diode}
{dragging:drg}
{file -- f9:f9}
{function generator}
{fuse}
{go}
{grid}
{ground}
{help -- f1:f1}
{inductor}
{label -- f6:f6}
{light-emitting diode:led}
{macro -- f5:f5}
{menu}
{mouse}
{move -- f4:f4}
{multimeter}
{opamp}
{oscilloscope}
{parts bin:bin}
{pointing:pnt}
{preferences -- f10:f10}
{print:prt}
{program controls:ctrl}
{quit}
{relay}
{resistor}
{rotate -- f8:f8}
{scrolling/scroll boxes:scrl}
{selecting:sel}
{show grid:sgr}
{show labels:slb}
{show values:svl}
{simulation:go}
{special keys:keys}
{spin selector:sps}
{steady state analysis:tsa}
{summary of analog simulation:sas}
{test instruments:inst}
{text fields:keys}
{tips}
{transformer}
{transient analysis:tsa}
{transient/steady state:tsa}
{transistor:xstr}
{useful formulas:crib}
{voltage sources:v}
{voltmeter}
{wiring:wir}
{workspace:wksp}
{zener diode}
{zoom -- f7:f7}
~f10||
Preferences -- F10
{transient/steady state:tsa}
{analog precision:apre}
{grid}
{show grid:sgr}
{show labels:slb}
{show values:svl}
~tsa||
Transient/Steady State
This controls the kind of analysis done and the
display of the waveform on the {oscilloscope}.
{transient:tra} {steady state:ssa}
~tra||
Transient analysis
Displays the initial response of the circuit and
stops the trace when the oscilloscope screen
fills. If a steady state is achieved before the
scope screen is filled, the steady-state waveform
will continue to fill it. In this mode,
redisplaying the scope will show only the first
cycle of the transient response.
~ssa||
Steady state analysis
Analysis continues until a steady state is
reached. The scope redraws each time the screen is
full. Some circuits may take many cycles to reach
stability. If you wish to observe a lengthy
transient response, select Steady State (even
though you cannot save and redisplay the
transient).
~apre||
Analog precision
You can control the degree of accuracy used to
compute the values of the {analog simulation:sim}
with the {spin selector:sps} on the
{Preferences:f10} menu.
Requiring less accuracy can speed up circuit
simulation. The smaller the percentage of
precision, the more accuracy will be computed. The
program defaults to the least precision and
greatest speed.
~sim||
Simulating analog circuits
{■ summary of simulation:sas}
{■ error conditions:err}
After you build a circuit, you can test it by
simulating its activity. Electronics Workbench
solves a set of equations to find all the current,
voltage and resistance values in the circuit at
many points over an interval of time. The test
instruments let you {read the values:sm1}.
Use the {Preferences:f10} menu to choose between:
{■ transient analysis:tra}
{■ steady state analysis:ssa}
The analysis chosen affects the operation of the
{oscilloscope}.
When anything in the circuit is changed
(components removed or inserted, values of
components changed, settings on the function
generator changed) the analysis is no longer valid.
~sm1||
Reading test points
After simulation is complete, the {instruments:ilst}
will display the values and waveforms of the
signal at any node in the circuit. As long as the
simulation is valid, that is, as long as the
circuit has not changed, the wires from the
{oscilloscope} and the {multimeter} may be moved
to any connection point on the circuit to display
the values.
The oscilloscope redraws itself whenever its
probes are moved; it displays present values at
all nodes in the circuit without having to press
GO again.
It is good practice to insert {connectors:connector}
in wires at various points in your circuit so you
can read values there.
The old values remain at each node in the circuit
even after changes are made in the circuit, so if
you accidentally clip a wire and restore it, the
values can still be read. (This feature is provided
because the mathematics of simulating a circuit can
take a long time, especially with a complex
circuit.)
You can change the controls on the oscilloscope to
display the waveform at a different scale without
pressing GO again. Just click on AC/0/DC on either
channel to draw at the new settings.
Remember to click GO whenever anything in the
circuit is changed or the input to the circuit
from the {function generator} is changed.
~err||
Analog error conditions
If the circuit is improperly constructed, it
will not function and no mathematical
{simulation:sim} is possible. When this
happens, a confirmation box gives an error
message that may help you find the problem.
You must determine by inspection the cause of
the failure.
Sometimes there is not enough memory to
complete the operation.
~sas||
Summary of analog simulation
Analog simulation always requires {GO} to simulate
the circuit.
The values remain in place at the nodes of the
circuit and remain true for that configuration.
To see the effect of changes in the circuit, you
must press GO again.
{■ details:sim} {■ errors:err}
~com||
Analog components
{ac current}
{ac voltage}
{ammeter}
{battery}
{bulb}
{capacitor}
{connector}
{current sources:ctsc}
{dc current}
{diode}
{fuse}
{ground}
{inductor}
{led}
{operational amplifier:opamp}
{relay}
{resistor}
{transformer}
{transistors:xstr}
{voltage sources:v}
{voltmeter}
{zener diode}
~bulb||
Bulb
The light bulb is a {resistive:r}
component that dissipates energy
in the form of light. Specify its
power rating in watts.
~fuse||
Fuse
This {resistive:r} component serves to
protect against power surges and
overloads in circuitry. If the {current:mrcs}
exceeds the specified maximum (Imx, in
Amps) the fuse will open ("blow") and
cut off the current flow.
~relay||
Relay
The magnetic relay is a {coil:mrin} with a
specified inductance (Lc, in Henries) that
will cause a contact to open or close when a
specified {current:mrcs} (Ion, in A) charges it.
The contact will remain in the same position
until the current falls below the holding
value (Ihd, in A), when the contact will
return to its original position.
~ac current||
AC current source
The alternating {current source:ctsc} in the
analog {parts bin:bin} may be adjusted to any
{value:f6}. The number is the RMS value of
the signal.
Set its frequency on the {function generator}.
~ac voltage||
AC voltage source
The alternating current {voltage source:v}
in the analog parts bin may be adjusted to
any {value:f6}. The number is the RMS value
of the signal.
Set its frequency on the {function generator}.
~ammeter||
Ammeter
The ammeter in the parts bin allows you to
measure {current:mrcs} flow within the circuit.
Insert meters in the circuit (in series
with the flow being measured) wherever you
wish a reading. You can use as many meters
as you wish.
The internal resistance is controlled by
the setting of the {multimeter} using {F6}.
~battery||
Battery
The battery serves as a d.c. {voltage source:v} that
is completely {adjustable:f6} in this program.
{more about batteries:mrbt}.
~mrbt||
Batteries -- background information
A battery is a single electrochemical cell, or a
number of electrochemical cells wired in series,
used to provide a direct source of {voltage:v}
and/or {current:ctsc}.
The single cell has an approximate voltage of 1.5
Volts, depending on its construction. It consists
of a container of acid in which an electrode is
placed. Chemical action causes electrons to flow
between the electrode and the container, and this
creates a potential difference between the
electrode and the material of the container.
Batteries can be rechargeable, and can be built to
deliver extremely high currents for long periods.
The automobile ignition battery is an application
of a battery as a "current source"; the voltage
may vary considerably under use, with no visible
battery deterioration.
Batteries may be used as voltage references, their
voltage remaining stable and predictable to many
figures of accuracy for many years. The standard
cell is such an application. A standard cell is a
voltage source, and it is important that current
is not drawn from the standard cell.
~capacitor|c||
Capacitor
The {value:f6} of a capacitor may be adjusted
as desired.
A capacitor stores electric energy, affecting
a.c. relative to capacitance and a.c. frequency
and d.c. depending on capacitance alone.
{more about capacitors:mrcp}
~mrcp||
Capacitors -- background
Capacitors in an a.c. circuit behave as "short
circuits" to a.c. signals. They are widely used to
filter or remove a.c. signals from a variety of
circuits--a.c. ripple in d.c. power supplies, a.c.
noise from computer circuits, etc.
Capacitors prevent the flow of direct {current:ctsc}
in a d.c. circuit. They can be used to block
the flow of d.c., while allowing a.c. signals
to pass. Using capacitors to couple one circuit
to another is a common practice.
Capacitors take a predictable time to charge
and discharge and can be used in a variety of
time-delay circuits. They are in some ways
similar to {inductors:inductor} and are often
used with them for this purpose.
The basic construction of all capacitors involves
two metal plates separated by an insulator.
Electric current cannot flow through the
insulator, so more electrons pile up on one plate
than the other. The result is a difference in
{voltage:v} level from one plate to the other.
~ctsc||
Current source
Sources of a.c. and d.c. current are provided in
the {parts bin:bin}. Their values may be adjusted by
selecting {label:f6} from the {menu}.
{more about current sources:mrcs}
Current is calculated as follows:
E
I = ─────
R
~mrcs||
Current -- background
Alternating or direct current comes from a power
supply to a load, where the output {voltage:v} of
the supply is not important (and may, in fact, be
very low).
Most modern d.c. power supplies, using electronic
control of the output level, can be used as either
{voltage sources:v} or current sources. When the
load on the power supply becomes very heavy (a
small load resistance) these supplies will switch
from a voltage supply to a current supply.
Bipolar {transistors:xstr} are current-based. They
can be treated as low impedance current sources
for circuit analysis purposes.
Current sources are often used as signal sources
during the analysis of electric networks if there
is more concern about the currents flowing into
and out of a point than about the voltage
appearing across a component.
In general, current sources are associated with
low impedance circuits, while voltage sources are
associated with high impedance circuits.
~dc current||
DC current source
The direct {current source:ctsc} may be adjusted to any
{value:f6} by using {Label:f6} from the {menu} or {F6}.
{more about current sources:ctsc}
~diode|di||
Diode
A supply of general purpose diodes is
included in the {parts bin:bin}. You can
adjust the {value:f6} of several parameters
to change the characteristics of the device.
{more about diodes:mrdi}
~mrdi||
Diodes -- background
A diode is the simplest form of solid state
switch, being either open (not conducting), or
closed (conducting).
These solid state components conduct electric
{current:ctsc} very easily in one direction, while
conducting current very poorly in the opposite
direction.
Diodes exhibit a number of useful characteristics,
such as predictable capacitance (that can be
{voltage:v} controlled) and a region of very stable
voltage. Diodes can, therefore, be used as voltage
controlled {capacitors:c} (varactors) and voltage
references (zener diodes).
Because diodes will conduct current easily in only
one direction, they are used extensively as power
rectifiers, converting a.c. signals to pulsating
d.c. signals, for both power applications and
radio receivers.
Diodes behave as voltage controlled switches, and
have replaced mechanical switches and relays in
many applications where remote signal switching is
done.
Even indicator lamps are now replaced with diodes
({LEDs:led}) that emit light in a variety of colors
when conducting.
A special form of diode, called a {zener diode},
is useful for voltage regulation.
~led||
Light-Emitting Diode
The Light-Emitting {Diode} emits visible
light when conducting {current:ctsc} in
the "forward" direction (current exceeds
Ion in Amps).
An LED is available in the digital {parts bin:bin}
for use as a probe. For this operation it requires
no external load {resistor} or ground connection,
though practical circuits must supply them.
{more about LEDs:ledinf}
~ledinf||
LED general information
LEDs are constructed of Gallium Arsenide or
Gallium Arsenide Phosphide. While efficiency can
be obtained when conducting as little as 2
milliAmperes of current, the usual design goal
is in the vicinity of 10 mA. During conduction,
there is a {voltage:v} drop across the diode of
about 2 volts.
Most early information display devices required
power supplies in excess of 100 volts. The LED
ushered in an era of information display components
with sizes and operating voltages compatible with
solid state electronics. Until the low-power
Liquid-Crystal Display was developed, LED displays
were common, despite high current demands, in
battery-powered instruments, calculators, and
watches. They are still commonly used as on-board
annunciators, displays, and solid state indicator
lamps.
~zener diode||
Zener diode
Zener diodes are special diodes designed to
continue operation within the reverse breakdown
area, beyond the Peak Inverse Voltage rating of
normal diodes. For zener diodes, this reverse
breakdown voltage is called the zener voltage
(V▀), which can range between 2.4 V and 200 V.
Zener diodes are used primarily in circuits
for voltage regulation.
{more about diodes:mrdi}
~inductor||
Inductor
The {value:f6} of an inductor may be set as
necessary.
{more about inductors:mrin}
~mrin||
Inductors -- background information
A coil of wire, of one "turn" or more, an inductor
stores energy in an electromagnetic field.
Inductors develop an electromagnetic field when
{current:ctsc} through them changes. Inductors
react to being placed in a changing magnetic field
by developing an "induced" {voltage:v} across the
turns of the inductance, and will provide current
to a load across the inductance. Voltages can be
very large.
Inductors are similar to {capacitors:c} in storing
energy in electric fields, and their "charge" and
"discharge" times make them useful in time delay
circuits.
Electric transformers take advantage of the
transfer of energy in a magnetic field from the
primary winding to the secondary winding, using
induced voltage and current. The transfer is
proportional to the ratio of the winding turns.
Radio antennae are inductors, and operate exactly
like transformers in generating electromagnetic
fields and in detecting them. Efficiency is
proportional to size.
The ignition coil in an automobile develops a very
high induced voltage when the current through it
suddenly becomes very great. This is the voltage
that fires spark plugs.
~opamp||
Operational amplifier
A supply of operational amplifiers is
included in the {parts bin:bin}. You can
adjust the {value:f6} of several parameters
to change the characteristics of the device.
{more about opamps:mrop}
~mrop||
Opamps -- general
The operational amplifier is a high gain
block based upon the principle of a
differential amplifier. It is common to
applications dealing with very small input
signals.
The open loop gain (A) is typically very
large (10e5 to 10e6). Applying a
differential input across the opamp
terminals (+, -), the output voltage will
be: v╪█▄ = A * (v+ - v-).
The differential input must be kept small,
since the opamp saturates for larger
signals. The output voltage will not exceed
the value of the positive and negative power
supplies (Vp), also called the rails, which
vary typically from ±5V to ±15V. This
property is often used in alarm systems, to
trigger an alarm when a signal exceeds a
certain value (called a Schmitt trigger).
The operational amplifier is also used in
feedback circuits. With the correct
combination of resistors, both inverting and
non-inverting amplifiers of any desired gain
can be constructed.
Other properties of the opamp include a high
input resistance (Ri), and a very small
output resistance (Ro). Large input
resistance is important so that the opamp
does not place a load on the input signal
source. Due to this characteristic, opamps
are often used as front-end buffers to
isolate circuitry from critical signal
sources.
In analyzing circuits containing operational
amplifiers, it is best to assume all
amplifiers are ideal. The six
characteristics of an ideal amplifier
include:
1. infinite open loop gain (A)
2. infinite input resistance (Ri)
3. zero output resistance (Ro)
4. infinite bandwidth
5. differential input voltage of zero,
i.e. v+ = v-
6. zero current flow into either input
terminal.
~resistor||
Resistor
The {value:f6} of a resistor may be adjusted as
desired.
{about resistance and Ohm's law:r}
{more about resistors:mrr}.
~r||
Resistance
Ohm's Law states that {current:ctsc} flow depends on
circuit resistance:
I = E/R
Circuit resistance can be calculated from the
current flow and the {voltage:v}:
R = E/I.
Circuit resistance can be increased by connecting
resistors in series:
R▄ = R░ + R▒ +...+ R╫
Circuit resistance can be reduced by placing one
resistor in parallel with another:
1
R▄ = ──────────────────
1 1 1
─── + ─── + ───
R░ R▒ R╫
Resistors come in a variety of sizes, related to
the power they can safely dissipate. This can be
calculated:
P = I²R
{more about resistors:mrr}
~mrr||
Resistors -- general information
Color coded stripes on the resistor body specify
resistance, and the tolerance of resistance
accuracy. Larger resistors have these
specifications printed on them.
Any electrical wire has resistance, depending on
its material, diameter, and length. Wires that
must conduct very heavy currents ({ground} wires
on lightning rods, for example) have large
diameters, to reduce resistance.
The power dissipated by a resistive circuit
carrying electric current is in the form of
heat. Circuits dissipating excessive energy
will literally burn up. Practical circuits
must take power capacity into account.
~transformer||
Transformer
You can adjust the model parameters of the
transformer using {F6}.
For the simulation to work properly, both
sides of the transformer must have a common
reference point, which may be ground.
Transformers are one of the most common and
useful applications of {inductance:mrin}.
~npn bjt||
NPN transistor
The NPN bipolar transistor has generic
values suitable for most circuits. These
values may be changed by clicking on Modify
Parameters from the {label:f6} box.
{more about transistors:xstr}
~pnp bjt||
PNP transistor
The PNP bipolar transistor has generic
values suitable for most circuits. These
values may be changed by clicking on Modify
Parameters from the {label:f6} box.
{more about transistors:xstr}
~xstr||
Transistors
Bipolar transistors are current-based valves used
for controlling electronic {currents:ctsc}. They are
made from silicon or germanium, with some
"impurity" materials added to facilitate current
flow.
Bipolars come in two versions: {PNP:pnp bjt} and {NPN:npn bjt}.
They have different power supply polarities and
different internal current flow directions. The
letters refer to the polarities (Positive/Negative)
of the materials making up the transistor
"sandwich."
Transistors are operated in three different
configurations depending on which element is
common to input and output: common base, common
emitter and common collector. The three modes have
different input and output impedances, different
gains and offer individual advantages to the
designer.
The transistor began the solid state phase of
electronics, and they still play an important part
in it. Their small size made "chip" technology
possible; even small ICs may contain many
transistors. Transistors make {battery} power
practical for instruments and communicators,
allowing very complex systems to be made light and
portable.
~v||
Voltage source
A power or signal source where the chief concern
is the output voltage.
D.c. power sources must supply voltage with good
"regulation"--freedom from voltage drop with
changes in load or line, and freedom from noise
and a.c. ripple in the voltage output.
An a.c. voltage source, as a power source or as a
signal generator, must provide a waveform free of
distortion--the waveform must contain only the
fundamental frequency of the a.c. generator, and
no multiple frequencies, called "harmonics".
If a voltage source is used as a variable-
frequency signal generator, its output impedance
must remain constant as the frequency varies in
order to avoid a varying output voltage. In many
voltage signal sources, it is also important
that the output frequency remain highly stable.
A voltage source is often used in the analysis of
electric networks, if the emphasis is on voltages
appearing across components, rather than on
{current:ctsc} flowing into and out of points in the
circuit.
~voltmeter||
Voltmeter
The voltmeter in the parts bin allows you to
measure {voltage:v} differences between
points in the circuit. Insert meters in the
circuit (in parallel with the points being
measured) wherever you wish a reading. You
can use as many meters as you wish.
The internal resistance is controlled by
the setting of the {multimeter} using {F6}.
~ilst||
Analog instruments
{function generator}
{multimeter}
{oscilloscope}
{Bode plotter}
~multimeter||
Multimeter
Use the multimeter to measure electrical signals
and components to determine {voltage:v},
{current:ctsc} or {resistance:r} between two
points in the circuit.
{general info:inst} {adjusting the controls:ajm}
~ajm||
Multimeter controls
{AMP:mm1} {VOLT:mm2} {OHM:mm3} {dB:mm4}
{AC:mm5} {DC:mm6}
{-:mm7} {+:mm8}
~mm1||
AMP -- multimeter
Displays the {current:ctsc} through the circuit
at the test point. The instrument must be inserted
into the circuit to measure current flow. Note
that it is not possible to switch from measuring
voltage across points of the circuit to measuring
current in the circuit without connecting the
multimeter appropriately, clicking the AMP button,
and clicking {GO} to activate the new
configuration.
~mm2||
VOLT -- multimeter
Measures the {voltage:v} difference between any
two points in the circuit. After the circuit has
been simulated with GO, the points of connection
may be moved around to test values at any node in
the circuit.
~mm3||
OHM -- multimeter
Measures {resistance:r} between the points of
connection. Note that a part cannot be in a closed
circuit to get an accurate measurement. Total
resistance between points in a resistive network
may be measured.
~mm4||
dB -- multimeter
Measures potential difference between two points
in the circuit and displays it as decibels of
loss.
~mm5||
AC [sine wave symbol] --
This button causes the meter to display root mean
square values of an alternating signal.
~mm6||
DC [straight line symbol] --
This button causes the meter to display the
instantaneous direct current value of a signal.
~mm7||
"-" -- multimeter
The negative terminal.
~mm8||
"+" -- multimeter
The positive terminal.
~function generator||
Function generator
The function generator is a {voltage source:v} that
supplies analog signals in the form of sine, square
and triangular waves.
{general info:inst} {adjusting the controls:ajf}
~ajf||
Function generator controls
{waveform:fg1}
{frequency:fg2}
{duty cycle:fg3}
{symmetry:fg4}
{amplitude:fg5}
{offset:fg9}
{+:fg6} {COM:fg7} {-:fg8}
{spin selectors:sps} {text fields:keys}
~fg1||
Waveform -- function generator
Click on the sine wave, the triangular wave, or
the square wave to control the output waveform.
~fg2||
Frequency -- function generator
The frequency value can be {spin selected:sps} from
1 to 999 and the units can spin from Hz to MHz.
~fg3||
Duty cycle -- function generator
Duty cycle can spin from 1 to 99 percent and
affects the shape of the square and triangular
waves. For square waves this controls the
proportion of the cycle that is high. 50% duty
gives square waves with high and low parts equal.
For triangular waves this controls the slope by
shifting where in the cycle the peak is. 50% duty
gives triangular waves with equal slope for the
rise and fall.
~fg4||
Symmetry -- function generator
Symmetry controls the amount of signal generated
above and below the d.c. level of the signal.
Values range from 0 to 100%, where 50% provides
rms symmetry about the d.c. level (i.e. positive
and negative peaks are the same distance from the
offset).
~fg5||
Amplitude -- function generator
Amplitude controls the value of the wave from its
d.c. level to its peak value. This is the same as
the difference between the COM and + or -
terminals. If the output leads are connected to
COM and to + or -, the peak to peak measurement of
the wave equals twice the amplitude value. If the
output comes from + and -, the peak-to-peak value
will be four times the amplitude value. Offset
controls the d.c. level about which the
alternating signal varies.
The units value for Amplitude applies to the
offset as well.
Note that the Amplitude is a peak reading,
while the values of the alternating sources
in the parts bin are RMS values.
~fg6||
"+" -- function generator
Provides a signal with the selected amplitude in
the positive direction from neutral COM.
~fg7||
COM -- function generator
Provides a reference level signal.
~fg8||
"-" -- function generator
Provides a signal with the selected amplitude in
the negative direction from neutral COM.
~fg9||
Offset -- function generator
This controls the amount of DC applied to the
output signal.
~oscilloscope||
Oscilloscope
The oscilloscope displays the amplitude and
frequency variations of electronic signals.
{general info:inst} {adjusting the controls:ajo}
~ajo||
Oscilloscope controls
{spin selectors:sps} {text fields:keys}
{TIME BASE:os1} {GROUND:os3}
{X POS:os2} {TRIGGER:os4}
{Y SCALE [ /DIV ]:os5}
{Y POS:os6}
{AC | 0 | DC:os7}
The oscilloscope has two input channels,
A and B, allowing two different signals to be
displayed simultaneously. These controls are on
the lower right of the scope face.
If the {simulation:sim} is still valid, you can
move the probes from the oscilloscope to another
node. -- just click on AC or DC to redraw the
scope face with the new signal.
~os1||
TIME BASE -- oscilloscope
The TIME BASE (x-axis on the display) must be
adjusted relative to the signal frequency to get
a readable display. The TIME BASE box is a
{spin selector:sps} with values ranging from 0.1
nanoseconds to 0.5 seconds per horizontal
division. Thus if you want to see one cycle of a
1000 Hertz signal, the TIME BASE should be 0.1
milliseconds. One cycle at 10 KHz requires a TIME
BASE of 0.01 milliseconds.
~os2||
X POS -- oscilloscope
The value at X POS may be used to move the
trigger point along the x-axis. Note that the
vertical scale on the reticle of the scope does
not cross at zero on the x-axis. The trigger
point is at the left edge of the display when the
X POS is zero.
~os3||
GROUND -- oscilloscope
The ground symbol indicates where {ground} should
be connected on the scope icon. The oscilloscope
must be attached to a ground reference point in
the circuit for accurate displays.
~os4||
TRIGGER -- oscilloscope
Triggering controls when the waveform begins to
display. You can set this to start the trace
on the positive or negative slope of the input
signal on channel A, channel B, or an external
signal. The external trigger signal must be
attached to the terminal on the scope icon. The
level of the signal at which the display triggers
can be set with the spin selector.
Tip: If you don't get a trace when you think you
should, check the triggering. You can always
attach the trigger to ground to effectively keep
it on.
~os5||
Y SCALE [/DIV] -- oscilloscope
You can adjust the value of the vertical divisions
and the origin on the y-axis independently for
each channel with their spin selectors. To get a
readable display you must adjust the y-scale
appropriately. An input signal of 1 volt will fill
the screen of the oscilloscope vertically if the
y-axis is set to 0.1 volts/division.
~os6||
Y POS -- oscilloscope
If you want to separate channels A and B by some
vertical distance to compare their waveforms, spin
select the y-position for each channel to move its
display up or down the screen.
~os7||
AC DC -- oscilloscope
Each channel may be switched to show the AC
component of the signal or the sum of DC and the
AC components. Selecting 0 shows a flat line at
the origin set by Y POS.
~bode plotter||
Bode plotter
The Bode plotter will plot the frequency
response of circuits as amplitude against
frequency.
Attach VI to the input and VO to the output of
the circuit. There must be a power source in
the circuit in addition to the plotter.
{general info:inst} {adjusting the controls:ajb}
~ajb||
Bode plotter controls
After zooming the face of the instrument open,
set the initial and final frequency and amplitude
by using the respective {spin selectors:sps}. The
mode of plotting can be switched from logarithmic
to linear on each scale by clicking on the correct
buttons.
You can read the frequency and amplitude of any
point on the waveform by moving the crosshairs to
it. Move the crosshairs by clicking on the arrow
buttons on the instrument face. You can also pick
the crosshairs up with the mouse and move them on
the plotter screen.
~crib||
Useful formulas
Ohm's Law:
I = E/R E = IR R = E/I
______________________________________________
Power: ┌─────
P = I²R I = √(P/R) R = P / I²
_____________________________________________
Resistance:
Series R = R░ + R▒ + R▓ + ...
1
Parallel R = ────────────────
1 1 1
── + ── + ── + ...
R░ R▒ R▓
V╘╫ R░
Attenuation: V╪█▄ = ───────
R░ + R▒
______________________________________________
Capacitance:
Parallel C = C░ + C▒ + C▓ + ...
1
Series C = ────────────────
1 1 1
── + ── + ── + ...
C░ C▒ C▓
______________________________________________
Capacitive Reactance: X╤ ═ 1/(2πfC)
Inductance:
Serial L = L░ + L▒ + L▓ + ...
Parallel L = ───────────────────
1 1 1
── + ── + ── + ...
L░ L▒ L▓
Inductive Reactance: X╘ = 2πfL
______________________________________________
Resonance:
1 1 1
f = ───────── L = ───────── C = ─────────
┌──
2π √LC 2π²f²C 2π²f²L
Circuit Quality:
Q = X/R = f/bandwidth
─────────────────────────────────────────
Transformer Turns Ratio:
a ═ primary turns/secondary turns
a ═ primary Volts/secondary Volts
a ═ secondary Amps/primary Amps
┌─────────────────────
a ═ √(Zprimary/Zsecondary)
